{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "view-in-github"
   },
   "source": [
    "<a href=\"https://colab.research.google.com/github/NeuromatchAcademy/course-content/blob/master/tutorials/W1D3_ModelFitting/student/W1D3_Tutorial7.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "fDXAYdIHuyCV"
   },
   "source": [
    "\n",
    "# Neuromatch Academy: Week 1, Day 3, Tutorial 7\n",
    "# Model Selection: AIC & cross validation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "aCD9LPJ7amih"
   },
   "source": [
    "#Tutorial Objectives\n",
    "\n",
    "This is Tutorial 7 of a series on fitting models to data. We start with simple linear regression, using least squares optimization (Tutorial 1) and Maximum Likelihood Estimation (Tutorial 2). We will use bootstrapping to build confidence intervals around the inferred linear model parameters (Tutorial 3). We'll finish our exploration of linear models by  generalizing to multiple linear regression (Tutorial 4). We then move on to polynomial regression (Tutorial 5). We end by learning how to choose between these various models. We discuss the bias-variance trade-off (Tutorial 6) and two common methods for model selection, AIC and Cross Validation (Tutorial 7).\n",
    "\n",
    "In this tutorial, we will learn about model selection and two methods to accomplish model selection (AIC and cross-validation).\n",
    "\n",
    "Tutorial objectives:\n",
    "\n",
    "* Implement AIC and use it to compare polynomial regression models\n",
    "\n",
    "* Implement cross-validation and use it to compare polynomial regression model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "cellView": "form",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 518
    },
    "colab_type": "code",
    "id": "vYGJZXA9wKSF",
    "outputId": "811e5083-5316-411c-ab70-3b86f1bd9482"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Video available at https://youtube.com/watch?v=EZAiR2frE7Y\n"
     ]
    },
    {
     "data": {
      "image/jpeg": "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\n",
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"854\"\n",
       "            height=\"480\"\n",
       "            src=\"https://www.youtube.com/embed/EZAiR2frE7Y?fs=1\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x7f7e985dcbd0>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#@title Video Cross-Validation\n",
    "from IPython.display import YouTubeVideo\n",
    "video = YouTubeVideo(id=\"EZAiR2frE7Y\", width=854, height=480, fs=1)\n",
    "print(\"Video available at https://youtube.com/watch?v=\" + video.id)\n",
    "video"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "QWj51UczQ2av"
   },
   "source": [
    "# Setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "cellView": "form",
    "colab": {},
    "colab_type": "code",
    "id": "JXOrOqhQRDSi"
   },
   "outputs": [],
   "source": [
    "#@title  Imports\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.model_selection import KFold"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "cellView": "form",
    "colab": {},
    "colab_type": "code",
    "id": "W25y2KDnYRgN"
   },
   "outputs": [],
   "source": [
    "#@title Figure Settings\n",
    "%matplotlib inline\n",
    "fig_w, fig_h = (8, 6)\n",
    "plt.rcParams.update({'figure.figsize': (fig_w, fig_h)})\n",
    "%config InlineBackend.figure_format = 'retina'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "cellView": "form",
    "colab": {},
    "colab_type": "code",
    "id": "-i1swxnYRQ-B"
   },
   "outputs": [],
   "source": [
    "#@title Helper functions\n",
    "def ordinary_least_squares(x, y):\n",
    "  \"\"\"Ordinary least squares estimator for linear regression.\n",
    "\n",
    "  Args:\n",
    "    x (ndarray): design matrix of shape (n_samples, n_regressors)\n",
    "    y (ndarray): vecto\"r of measurements of shape (n_samples)\n",
    "  \n",
    "  Returns:\n",
    "    ndarray: estimated parameter values of shape (n_regressors)\n",
    "  \"\"\"\n",
    "  return np.linalg.inv(x.T @ x) @ x.T @ y\n",
    "\n",
    "def make_design_matrix(x, order):\n",
    "  \"\"\"Create the design matrix of inputs for use in polynomial regression\n",
    "  \n",
    "  Args:\n",
    "    x (ndarray): An array of shape (samples,) that contains the input values.\n",
    "    max_order (scalar): The order of the polynomial we want to fit\n",
    "\n",
    "  Returns:\n",
    "    numpy array: The design matrix containing x raised to different powers\n",
    "  \"\"\"\n",
    "\n",
    "  # Broadcast to shape (n x 1) if shape (n, ) so this function generalizes to multiple inputs\n",
    "  if x.ndim == 1:\n",
    "    x = x[:,None]\n",
    "\n",
    "  #if x has more than one feature, we don't want multiple columns of ones so we assign\n",
    "  # x^0 here\n",
    "  design_matrix = np.ones((x.shape[0],1)) \n",
    "\n",
    "  # Loop through rest of degrees and stack columns\n",
    "  for degree in range(1, order+1):\n",
    "      design_matrix = np.hstack((design_matrix, x**degree))\n",
    "\n",
    "  return design_matrix\n",
    "\n",
    "\n",
    "def solve_poly_reg(x, y, max_order):\n",
    "  \"\"\"Fit a polynomial regression model for each order 0 through max_order.\n",
    "  \n",
    "  Args:\n",
    "    x (ndarray): An array of shape (samples, ) that contains the input values \n",
    "    y (ndarray): An array of shape (samples, ) that contains the output values\n",
    "    max_order (scalar): The order of the polynomial we want to fit\n",
    "\n",
    "  Returns:\n",
    "    numpy array: (input_features, max_order+1) Each column contains the fitted \n",
    "    weights for that order of polynomial regression\n",
    "  \"\"\"\n",
    "\n",
    "  # Create a dictionary with polynomial order as keys, and np array of theta \n",
    "  # (weights) as the values\n",
    "  theta_hat = {}\n",
    "\n",
    "  # Loop over polynomial orders from 0 through max_order\n",
    "  for order in range(max_order+1):\n",
    "\n",
    "    X = make_design_matrix(x, order)\n",
    "    this_theta = ordinary_least_squares(X, y)\n",
    "\n",
    "    theta_hat[order] = this_theta\n",
    "\n",
    "  return theta_hat\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "YKG1_6gSkHFU"
   },
   "source": [
    "# Model Selection\n",
    "\n",
    "We now have multiple choices for which model to use for a given problem: we could use linear regression, order 2 polynomial regression, order 3 polynomial regression, etc. As we saw in Tutorial 6, different models will have different quality of predictions, both on the training data and on the test data. We need to be able to choose between models without looking at any test data. In fact, we should never look at or use the test data in any way when modeling.  If we do, we would then be unable to report a true indication of how well the model generalizes to new data. We will cover two different methods for model selection in the next two sections. We will explore both methods using the same train/test data and polynomial regression models as in Tutorial 6 (generated below)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "VliUfiNPSiiG"
   },
   "outputs": [],
   "source": [
    "# You've seen this code before!\n",
    "\n",
    "### Generate training data\n",
    "np.random.seed(0)\n",
    "n_samples = 50\n",
    "x_train = np.random.uniform(-2, 2.5, n_samples) # sample from a uniform distribution over [-2, 2.5)\n",
    "noise = np.random.randn(n_samples) # sample from a standard normal distribution\n",
    "y_train =  x_train**2 - x_train - 2 + noise\n",
    "\n",
    "### Generate testing data\n",
    "n_samples = 20\n",
    "x_test = np.random.uniform(-3, 3, n_samples) # sample from a uniform distribution over [-2, 2.5)\n",
    "noise = np.random.randn(n_samples) # sample from a standard normal distribution\n",
    "y_test =  x_test**2 - x_test - 2 + noise\n",
    "\n",
    "### Fit polynomial regression models\n",
    "max_order = 5\n",
    "theta_hat = solve_poly_reg(x_train, y_train, max_order)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "kHKyP5i6qfXb"
   },
   "source": [
    "## Akaike's Information Criterion (AIC)\n",
    "\n",
    "In order to choose the best model for a given problem, we can ask how likely the data is under a given model. We want to choose a model that assigns high probability to the data. A commonly used method for model selection that uses this approach is **Akaike’s Information Criterion (AIC)**.\n",
    "\n",
    "Essentially, AIC estimates how much information would be lost if the model predictions were used instead of the true data (the relative information value of the model). We compute the AIC for each model and choose the model with the lowest AIC. Note that AIC only tells us relative qualities, not absolute - we do not know from AIC how good our model is independent of others.\n",
    "\n",
    "AIC strives for a good tradeoff between overfitting and underfitting by taking into account the complexity of the model and the information lost. AIC is calculated as:\n",
    "\n",
    "$$ AIC = 2K - 2 log(L)$$\n",
    "\n",
    "where K is the number of parameters in your model and L is the likelihood that the model could have produced the output data. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "GXBqn09emIdj"
   },
   "source": [
    "### AIC for Polynomial Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "F6i_20bomLCQ"
   },
   "source": [
    "Now we know what AIC is, we want to use it to pick between our polynomial regression models. We haven't been thinking in terms of likelihoods though - so how will we calculate L? \n",
    "\n",
    "As we saw in Tutorial 2, there is a link between mean squared error and the likelihood estimates for linear regression models that we can take advantage of. \n",
    "\n",
    "*Derivation time!*\n",
    "\n",
    "We start with our formula for AIC from above:\n",
    "\n",
    "$$ AIC = 2k - 2 log L $$\n",
    "\n",
    "For a model with normal errors, we can use the log likelihood of the normal distribution:\n",
    "\n",
    "$$ \\log L = -\\frac{n}{2} \\log(2 \\pi) -\\frac{n}{2}log(\\sigma^2) - \\sum_i^n \\frac{1}{2 \\sigma^2} (y_i - \\tilde y_i)^2$$\n",
    "\n",
    "We can drop the first and last terms as both are constants and we're only assessing relative information with AIC. Once we drop those terms and incorporate into the AIC formula we get:\n",
    "\n",
    "$$AIC = 2k + nlog(\\sigma^2)$$\n",
    "\n",
    "We can replace $\\sigma^2$ with the computation for variance (the sum of squared errors divided by number of samples). Thus, we end up with the following formula for AIC for linear and polynomial regression:\n",
    "\n",
    "$$ AIC = 2K + n log(\\frac{SSE}{n})$$\n",
    "\n",
    "where k is the number of parameters, n is the number of samples, and SSE is the summed squared error.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "ZqWlEviJ7rbf"
   },
   "source": [
    "#### Exercise: Compute and compare AIC"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 412
    },
    "colab_type": "code",
    "id": "wL1zAH7DqeUN",
    "outputId": "dea10eef-e384-4e29-d305-e0b267536b46"
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 406,
       "width": 526
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "AIC = np.zeros((max_order+1))\n",
    "for order in range(0, max_order+1):\n",
    "\n",
    "  # Compute predictions for this model \n",
    "  X_design = make_design_matrix(x_train, order)\n",
    "  y_hat = np.dot(X_design, theta_hat[order])\n",
    "\n",
    "  #####################################################################################################\n",
    "  ## TODO for students: Compute AIC for this order polynomial regression model\n",
    "  # 1) Compute sum of squared errors given prediction y_hat and y_train (SSE in formula above)\n",
    "  # 2) Identify number of parameters in this model (K in formula above)\n",
    "  # 3) Compute AIC (call this_AIC) according to formula above\n",
    "  #####################################################################################################\n",
    "\n",
    "    # Compute SSE\n",
    "    #residuals = YOUR CODE HERE\n",
    "    #sse = YOUR CODE HERE\n",
    "\n",
    "    # Get K\n",
    "    #K = len(theta_hat[order])\n",
    "\n",
    "\n",
    "    # Compute AIC\n",
    "    # AIC[order] = ...\n",
    "\n",
    "with plt.xkcd():\n",
    "  plt.bar(range(max_order+1), AIC);\n",
    "  plt.ylabel('AIC')\n",
    "  plt.xlabel('polynomial order')\n",
    "  plt.title('comparing polynomial fits')\n",
    "  plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 412
    },
    "colab_type": "text",
    "id": "kx8LtxGh067t",
    "outputId": "4f550177-f7cf-4cc8-9a6b-76bd387a3432"
   },
   "source": [
    "[*Click for solution*](https://github.com/NeuromatchAcademy/course-content/tree/master//tutorials/W1D3_ModelFitting/solutions/W1D3_Tutorial7_Solution_cf15e1ca.py)\n",
    "\n",
    "*Example output:*\n",
    "\n",
    "<img alt='Solution hint' align='left' width=508 height=406 src=https://raw.githubusercontent.com/NeuromatchAcademy/course-content/master/tutorials/W1D3_ModelFitting/static/W1D3_Tutorial7_Solution_cf15e1ca_0.png>\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "pXlhin28wHpe"
   },
   "source": [
    "Which model would we choose based on AIC? "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "EthmSy3RpLwQ"
   },
   "source": [
    "## Cross Validation\n",
    "\n",
    "AIC is just one method for model selection - another commonly used method is **cross validation**. AIC gives a measure of how likely the training data is given the model. Cross-validation takes a different approach to the model selection problem and asks how well the model predicts new data that it hasn't seen yet. \n",
    "\n",
    "Instead of looking at test data, we want to use held-out data set that will not be used for the final evaluation, **validation data**. We often have a limited amount of data though (especially in neuroscience), so we do not want to further reduce our potential training data by reassigning some as validation. Luckily, we can use **k-fold cross-validation**! In k-fold cross validation, we divide up the data into k subsets, train a model on k-1 subsets, and compute error on the held-out subset (our validation data). In total, we train k instances of each model. Each of these k instances has a different subset excluded from fitting and labeled as validation. We then average the error of each of the k trained models on its validation subset - this is the validation error of this model type. \n",
    "\n",
    "To make this explicit, let's say we have 1000 samples of training data and choose 4-fold cross-validation. Samples 0 - 250 would be subset 1, samples 250 - 500 subset 2, samples 500 - 750 subset 3, and samples 750-1000 subset 4. First, we train an order 3 polynomial regression on subsets 1,2,3 and evaluate on subset 4. Next, we train an order 3 polynomial model on subsets 1,2,4 and evalute on subset 3. We continue until we have 4 instances of a trained order 3 polynomial regression model, each with a different subset as validation data, and average the validation error from each instance.\n",
    "\n",
    "We can now compare the validation error of different models to pick a model that generalizes well to held-out data. We can choose the measure of prediction quality to report error on the validation subsets to suit our purposes. We will use MSE here but we could also use log likelihood of the data and so on. As a final step, we retrain this model on all of the training data (without subset divisions) to get our final model that we will evaluate on test data. This approach allows us to evaluate the quality of predictions on new data without sacrificing any of our precious training data. \n",
    "\n",
    "These steps are summarized in this diagram from SkLearn (https://scikit-learn.org/stable/modules/cross_validation.html)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "mVDh-wrQmBLU"
   },
   "source": [
    "![Diagram from Sklearn](https://scikit-learn.org/stable/_images/grid_search_workflow.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "oX6sVvpCh7GN"
   },
   "source": [
    "\n",
    "\n",
    "Importantly, we need to be very careful when dividing the data into subsets.  The validation subset should not be used in any way to fit the model. We should not do any preprocessing (e.g. normalization) before we divide into subsets or the validation subset could influence the training subsets. A lot of false-positives in crossvalidation come from wrongly dividing. \n",
    "\n",
    "An important consideration in the choice of model selection method are the relevant biases. If we just fit using MSE on training data, we will generally find that fits get better as we add more parameters because the model will overfit the data, as we saw in Tutorial 6. When using cross-validation, the bias is the other way round. Models with more parameters are more affected by noise so cross-validation will generally prefer models with fewer parameters.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "L4fyrY3vAmGC"
   },
   "source": [
    "### Exercise: implement cross-validation\n",
    "\n",
    "Given our set of models to evaluate (polynomial regression models with orders 0 through 5), we will use cross-validation to determine which model has the best predictions on new data according to MSE. \n",
    "\n",
    "In this code, we split the data into 10 subsets using `Kfold` (from `sklearn.model_selection`). `KFold` handles cross-validation subset splitting and train/val assignments.  In particular, the `Kfold.split` method returns an iterator which we can loop through. On each loop, this iterator assigns a different subset as validation and returns new training and validation indices with which to split the data. \n",
    "\n",
    "We will loop through the 10 train/validation splits and fit several different polynomial regression models (with different orders) for each split. You will need to use the `solve_poly_reg` method from Tutorial 5 (already implemented in this notebook)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "kTvzIvOozOfQ"
   },
   "outputs": [],
   "source": [
    "def cross_validate(x_train,y_train,max_order,n_splits):\n",
    "\n",
    "  # Initialize the split method\n",
    "  kfold_iterator = KFold(n_splits)\n",
    "\n",
    "  # Initialize np array mse values for all models for each split\n",
    "  mse_all = np.zeros((n_splits, max_order+1))\n",
    "\n",
    "  for i_split, (train_indices, val_indices) in enumerate(kfold_iterator.split(x_train)):\n",
    "      \n",
    "      # Split up the overall training data into cross-validation training and validation sets\n",
    "      x_cv_train = x_train[train_indices]\n",
    "      y_cv_train = y_train[train_indices]\n",
    "      x_cv_val = x_train[val_indices]\n",
    "      y_cv_val = y_train[val_indices]\n",
    "\n",
    "    #############################################################################\n",
    "    ## TODO for students: Fill in missing ... in code below to choose which data\n",
    "    ## to fit to and compute MSE for\n",
    "    #############################################################################\n",
    "\n",
    "      ## Fit models\n",
    "      #theta_hat = YOUR CODE HERE\n",
    "\n",
    "      # Compute MSE\n",
    "      mse_this_split = np.zeros((max_order+1))\n",
    "      #for order in range(0, max_order+1):\n",
    "        #X_design= \n",
    "        #y_hat = )\n",
    "        #mse_this_split[order] = \n",
    "\n",
    "      #mse_all[i_split] = mse_this_split\n",
    "\n",
    "  #comment this line once you've filled in the function\n",
    "  raise NotImplementedError(\"Student excercise: implement cross-validation\")\n",
    "  return mse_all"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cellView": "both",
    "colab": {},
    "colab_type": "text",
    "id": "mQQyT3oTCiBH"
   },
   "source": [
    "[*Click for solution*](https://github.com/NeuromatchAcademy/course-content/tree/master//tutorials/W1D3_ModelFitting/solutions/W1D3_Tutorial7_Solution_56c15a33.py)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "lmORzt0CzOYk"
   },
   "source": [
    "Use the following code to visualize the cross-validated MSE. Which polynomial order do you think is a better model of the data?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 403
    },
    "colab_type": "code",
    "id": "UwMTQ6U-cUL0",
    "outputId": "f31ca5d8-af2d-47b9-baab-8beb59df108c"
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 386,
       "width": 487
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "max_order = 5\n",
    "n_splits = 10\n",
    "mse_all = cross_validate(x_train,y_train,max_order,n_splits)\n",
    "\n",
    "plt.figure()\n",
    "plt.boxplot(mse_all, labels=np.arange(0,max_order+1))\n",
    "plt.xlabel('Polynomial Order')\n",
    "plt.ylabel('Validation MSE')\n",
    "plt.title(f'Validation MSE over {n_splits} splits of the data');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "aP6W9rOQBUOn"
   },
   "source": [
    "Which model would you choose based on cross-validation? Is it the same or different than what you would choose based on AIC?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "FohJAKL1Bkkd"
   },
   "source": [
    "# Summary\n",
    "\n",
    "We need to use model selection methods, such as AIC and cross-validation, to determine the best model to use for a given problem. \n",
    "\n",
    "AIC focuses on how likely the data is given the model. \n",
    "\n",
    "Cross-validation focuses on how well the model predicts new data."
   ]
  }
 ],
 "metadata": {
  "colab": {
   "collapsed_sections": [],
   "include_colab_link": true,
   "name": "NeuromatchAcademy_W1D3_Tutorial7",
   "provenance": [],
   "toc_visible": true
  },
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.7"
  },
  "toc-autonumbering": true
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
